English

Perfect matchings and derangements on graphs

Combinatorics 2019-10-14 v2

Abstract

We show that each perfect matching in a bipartite graph GG intersects at least half of the perfect matchings in GG. This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph, and in terms of derangements and permutations on graphs. We give several related results and open questions.

Keywords

Cite

@article{arxiv.1906.05908,
  title  = {Perfect matchings and derangements on graphs},
  author = {Matija Bucic and Pat Devlin and Mo Hendon and Dru Horne and Ben Lund},
  journal= {arXiv preprint arXiv:1906.05908},
  year   = {2019}
}
R2 v1 2026-06-23T09:53:14.155Z